The Expectations Hypothesis





Kerry Back

Forward Curve

  • The forward curve shows the prices of contracts for different delivery dates.

  • It shifts up and down over time as prices change.

  • Its slope can also change.

  • The front month price is the “spot price” - i.e., the price for (near) immediate delivery.

Gold Forward Curve

Gold forward curve on 1-24-2022.

Expectations hypothesis

  • The expectations hypothesis is: The futures price is equal to the market’s expectation of what the spot price will become.
  • Example: maybe the market expected on 1-24-2022 that gold would hit $2,000 in 8 years.
  • The expectations hypothesis is reasonable, though there is risk and there may be risk premia.

Expectations and the forward curve

  • Expectations affect not just the futures price but also today’s spot price.
  • Example: If we think gold will hit $2,000 in 8 years and it is trading at $500 today, then we should all be buying gold today (quadruple our money in 8 years).
  • This drives up the spot price to the point that we would only get a “normal” return on spot gold.

  • Ignoring risk and risk premia, if we think gold will hit $2,000 in 8 years, then today’s spot price should be \(\text{2,000} / (1+r)^8\).
  • So, futures in 8 years (2,000)should equal spot \(\times (1+r)^8\)
  • In fact, the forward curve should be rising by the factor \(1+r\) each year.

Contango

  • A market is in contango if the forward curve is upward sloping, as in the gold example.

  • In other words, you pay more for future delivery than in the spot market.

  • The term originates from deferring purchase of a stock. You had to pay a fee to postpone settlement.

  • Contango is natural, because of the time value of money. But, there are other factors.

Backwardation

  • A market is in backwardation in the opposite situation: the forward curve is downward sloping.

Stock Index Futures in Backwardation

S&P 500 forward curve on 1-24-2022

Backwardation and Expectations Hypothesis

  • According to the expectations hypothesis, the market expected stock prices to fall on 1-24-2022.
  • Did people expect to lose money on stocks?
  • No. Part of the stock return is the dividend. According to the expectations hypothesis, the market expected to earn the risk-free rate on stocks as dividends + capital gain.
  • Dividends > interest \(\Rightarrow\) capital gain < 0.

Summary

  • Expectations hypothesis is “futures price = expected future spot price.”
  • Expectations affect both the futures price and the spot price.
  • Markets can be in contango (rising futures price and futures > spot) or backwardation (falling futures price and futures < spot).